Neighbour Notes
Neighbour notes do not appear in Schenker's version of species counterpoint but are related to the passing note.
Whereas the passing motion (or linear progression) progresses from one consonant note of the harmonic unit to another, the neighbour note returns to the initial note.

In the first of these examples, the top line moves from C to its neighbour note D, and back again - the dissonant D therefore prolongs the repetion of C that happens either side of it.

Neighbour notes can prolong either the first, third or fifth degree of a triad (in the case of C major, C, E or G). They must be no more than a major second away from the note being prolonged - hence the name. Neighbour notes can also be incomplete - appearing either before or after the consonant note - an example of this can be found in Combinations.

Note the way that Schenkerian analyses are notated: there are no stems on the noteheads and a slur spans the linear unit or diminution in question. Stems, beams and minim noteheads are used at other stages of an analysis (see Notation Guide)

The neighbour notes above are in their most simple form and are dissonant with the harmonic unit which they are prolonging. As explained more fully in the section on fundamental structure, the greatest innovation of the Schenkerian analytical method is that it looks for these linear units deep behind the surface of the piece as well.

A neighbour note can appear behind the surface of the music when it is consonant as in the example below. The D is still a neighbour note prolonging the harmonic unit of a C major chord, but it is harmonised by the dominant of C - namely G:

Here the neighbour note is consonant with the dominant harmony (although it is still conceptually dissonant with the C); it can therefore give rise to its own diminutions. In the example below, the neighbour note D is itself prolonged by a neighbour note - E.

NB: In terms of Schenker's metaphor of the artist and nature, the D here is trying to be a tonic in its own right - to 'give birth' to its own diminutions. The artist is allowing this to happen but at some point he or she has to stop this process: if the E was made consonant and given a neighbour note and then the same thing happened with that neighbour note and so on, the passage would eventually become incomprehensible as tonal music.